The isolated plasma membrane of the human erythrocytes displays the same shape and shape transformations as the intact cells. It is therefore generally believed that the plasma membrane plays a dominant role in determining erythrocyte shape. The plasma membrane consists of a fluid lipid bilayer to the surface of which is attached a protein skeleton. The two halves of the lipid bilayer and the protein network (gel) are tighly coupled, but at the same time elastically deformable and can slide relative to one another in the plane of the cell membrane. The equilibrium shape of such a structure is determined by the combined mechano‐chemical properties of the individual layers and equals the cell shape that for the given cell volume corresponds to the lowest total elastic free energy. The elastic free energy of the lipid bilayer is mainly associated with bending and change in surface area for each of the two lipid monolayer. For the protein membrane skeleton the elastic free energy mainly equals the sum of the local contributions due to shear deformation and surface change. When the mechano‐chemical properties of each of the layers are known, calculation of the equilibrium shape is in principle just an exercise in standard continuum mechanics. The elastic properties of pure lipid monolayers have long been qualitatively fairly well known. The changes in lipid bilayer elastic properties resulting from the presence of integral membrane proteins have just recently become better understood. The detailed molecular basis for the elastic properties of the protein membrane skeleton remains unresolved despite many attempts to elucidate the problem. It is widely agreed that the elastic properties are largely accounted for by the highly elongated spectrin molecules, but whether the membrane skelton elasticity is mainly of entropic or entalphic origin is still unsettled.